Question
(a) Prove that if $\lambda \neq 0$ is a nonzero eigenvalue of the nonsingular matrix $A$, then $1 / \lambda$ is an eigenvalue of $A^{-1}$. (b) What happens if $A$ has 0 as an eigenvalue?
Step 1
If $\lambda$ is an eigenvalue of a matrix $A$, then there exists a nonzero vector $v$ such that $Av = \lambda v$. This vector $v$ is called an eigenvector corresponding to the eigenvalue $\lambda$. Show more…
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